Answer to Question #123755 in Abstract Algebra for Nii Laryea

Question #123755
Consider the set X = R \ {-1} with the binary relation * defined by x * y = x + y + xy.
Find the solution for the equation 5 * x * 2 = -19.
1
Expert's answer
2020-06-28T09:11:02-0400

We apply the operation once and receive: x * 2 = x+2+2x=3x+2. The second application yields

5 * (x * 2 )=5+3x+2+5(3x+2)=18x+17. One can check that it is associative. I.e.,

5 * (x * 2 ) = (5 * x ) * 2. The equation then reads 18x+17=-19. Solving the latter, we receive x=-2.

Answer: x=-2


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